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Abstract

Coupling between photonic-crystal defect microcavities is observed to result in a splitting not only of the mode wavelength but also of the modal loss. It is discussed that the characteristics of the loss splitting may have an important impact on the optical energy transfer between the coupled resonators. The loss splitting — given by the imaginary part of the coupling strength — is found to arise from the difference in diffractive out-of-plane radiation losses of the symmetric and the antisymmetric modes of the coupled system. An approach to control the splitting via coupling barrier engineering is presented.

The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (ΩA=ΩS) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of twohole barrier.

Other (5)

The flipping is the interference effect between two wave fronts arising from the coupling cavities. Depending on the PhC-lattice geometrical fill-factor, the flipping period does not correspond to nodes (ΩA=ΩS) at an integer number of holes in the barrier, which may accounts for larger splitting in the case of twohole barrier.

Figures (7)

Fig. 1. Illustration to the loss splitting and the energy transfer. (a) one-dimensional envelope functions (amplitudes) of the supermodes in space. (b) Time evolution of the supermode amplitudes (upper panel; note, AS(t) curve is shifted downwards for clarity) and the intensity in the coupled system within the “cavity 1” (|AS+AA|2) and within the “cavity 2” (|AS-AA|2) in the case of ΓS=ΓA. (c) time evolution in the case of ΓS≠ΓA

Fig. 5. 3D-FDTD simulated spectral response and Ey field distributions of the intentionally detuned L3 cavities (at fixed detuning). Note that the coupling strength is greatly reduced already for the triple-hole barrier, and the mode separation is marginally larger than for an infinite barrier (cavities computed separately). The Ey-field distributions in the case of the 3-hole barrier show slight mode delocalization, which indicates a very weak, but finite, coupling.

Fig. 6. Diffractive losses of the coupled-cavity system (3D FDTD analysis applied to disorder-free PhC structures). (a) E-fields of the symmetric (MS) and the antisymmetric (MA) modes in the reciprocal k-space (Fourier transforms at the reference plane above the membrane), for two coupled-cavity structures with different (one-hole, five-hole) barriers schematically illustrated on the right. The corresponding field pattern for the single L3 cavity is also shown, at the bottom. Leaky field components are situated within the air light cone (encircled area). Calculated from Eq. (3), the percentage of the integrated field intensity with k-vectors located inside the light cone is shown in the insets. (b) Real-space E-field patterns (absolute value) in the plane perpendicular to the membrane and along the symmetry axis (X) of the cavities for the structures of part (a), visualizing the radiation responsible for loss. The Q-factors, shown in the insets, were extracted directly from the 3D FDTD temporal response.

Fig. 7. Coupling and energy transfer design by PhC barrier engineering (3D FDTD analysis on disorder-free PhC structures). (a) Spectral response of the two coupled L3 cavities with increasing barrier length by adding holes. Geometry: the (normalized) radius of PhC holes is r/a=0.255, the lattice constant is a=210 nm. The field distributions (Ey) of the symmetric (MS, red) and the antisymmetric (MA, blue) modes are fully delocalized being essentially similar to the ones shown e.g. in the Fig. 3(c). (b) Adiabatic modification of the single-hole barrier by varying the radius of the separating hole from r/a=0 to 0.4. The trends are shown for both the mode frequencies (MA and MS solid curves, left axis) and their Q-factors (dashed curves, right axis). Crossing point ΓS=ΓA is indicated. The horizontal straight lines indicate the wavelength (solid) and the Q-factor (dashed) of an unperturbed L3 cavity. Vertical straight line indicates the close-to “experimental” case [i.e. compared to Fig. 3(a)]. (c) Calculated from Eq. (2), the time evolution of the field intensities in each cavity showing the energy transfer in the coupled system. The “experimental” case with loss splitting (upper panel) is compared to an optimized case (lower panel) where the losses can equalize (ΓS=ΓA). (d) 3D FDTD simulation of the PhC system that shows ΓS=ΓA : (left) time evolution of the probed field intensities (Hz component extracted from the two probes at the membrane center laterally positioned as shown on the sketch to the right); (right, bottom) cut by mirror symmetry, the in-plane near-field distributions (recorded in lg(1+|He|2) scale) corresponding to different moments in time (Media 1).